![]() ![]() ![]() The fractal dimension, D, is then related to the slope of the fitted line, as given in Table 4-6. If one wishes to use data in multiple directions, but anisotropy is not of interest, then the 2-D power spectrum can be calculated over the image area of interest, averaged azimuthally to yield an average radial power spectrum, and the fractal dimension calculated in the 1-D manner. This technique was used in Pentland (1984) to produce fractal maps from images. The fractal dimension was measured over 8-by-8 pixel blocks across the image, and the result used to segment the image into regions of different texture. Yamada, in Principles of Tissue Engineering (Fifth Edition), 2020 Geometryįractal geometry has provided a conceptual basis for identifying mechanisms that may underlie the formation of branches in biological settings. Fractal geometry has been applied to lung branching by considering the lung as a fractal object lacking characteristic scale and having self-similarity. Some of the modeling for lung geometry uses exponential models, starting with the premise that the lung is a dichotomous branch tree with a parental branch of greater length and diameter and an exponential decrease with every daughter branch due to maximizing entropy. Nevertheless, when this model was used to analyze more than 10 generations of branches, the exponential decrease could no longer accurately predict the diameter and length of subsequent branches. Therefore a renormalization model was developed in which the changes originally considered exponential were shown to be power-law decreases modulated by harmonic variation of the mean of the branch diameter. The fractal concept has been applied to many fields in medicine and in particular has found widespread application in the description of radiographic images. ![]()
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